(CNN) -- The Daily Show took a more serious turn Monday night when host Jon Stewart introduced his guest for the evening, Health and Human Services Secretary Kathleen Sebelius.

Sebelius, who has been on a media blitz in recent weeks as the individual mandate for the Affordable Care Act took effect October 1st, has appeared on multiple networks to promote the new law and to attempt to tamper criticism of its rollout.

As the secretary sat down to begin the segment, Stewart opened a laptop on his desk. "I'm going to attempt to download every movie ever, and you're going to try to sign up for Obamacare, and we'll see which happens first."

Sebelius admitted the website rollout "started a little rockier than we'd like," but said the administration had been working to make improvements. "It's better today than it was yesterday, and it will keep getting better."

The sign-up websites were offline for part of the weekend as efforts were made to fix multiple glitches that caused delays for many who attempted to use the program in the first few days.

When asked how many individuals had signed up for insurance so far, Sebelius admitted, "I can't tell you, because I don't know ... we will be giving monthly reports." She added that hundreds of thousands of accounts had been created, which indicated to the administration that those consumers "are going to go shopping" for insurance as the next step.

The segment became more contentious as Stewart turned to the subject of the individual mandate, specifically the fact that while many businesses were given a one-year delay to comply with the law, individuals were not.

"If I'm an individual that doesn't want this, it would be hard for me to look at a big business getting a waiver," Stewart said. "I would feel like you are favoring big business because they lobbied you ... but you're not allowing individuals that same courtesy."

Sebelius denied that was the case, but danced around answering the question directly, sticking instead to talking points.

After pressing her further on the issue to no avail, a somewhat exasperated Stewart finally smiled and asked, "Am I a stupid man?"

Later, as he threw to commercial, Stewart said he still was "not sure why individuals can't delay" and asked the secretary if he could keep asking her that same question when they returned.

Later, while addressing the issue of businesses cutting back hours for employees to avoid having to provide health care under the new regulations, Sebelius held firm. "Economists, not anecdotal folks, but economists, say there is absolutely no evidence that part-time work is going up. In fact, it's going down," she said. The secretary also said that for the first time ever, part-time employees in the United Sates would now have the option to purchase health insurance under the new law.

Toward the end, Stewart argued that a market-based strategy toward health care is a flawed concept in itself and that a single payer system would have been a more simple approach. But Sebelius jumped in, saying, "if we could have perhaps figured out a pathway, that may have been a reasonable solution."

"So this is jerry-rigged to deal with the crazy people?" Stewart asked.

"I think the president did not want to dismantle the health care that 85% of the country had," Sebelius responded.